Sharp Discounts Wholesale Club has two service desks, one at each entrance of th

Question

Sharp Discounts Wholesale Club has two service desks, one at each entrance of the store. Customers arrive at each service desk at an average of one every ten minutes. Sharp Discounts Wholesale Club is considering consolidating its two service desks into one location, staffed by two clerks. The clerks will continue to work at the same individual speed of three minutes per customer. Use Exhibit_7.12.

a. What is the probability of waiting in line? (Round your answer to 4 decimal places.)

b. How many customers, on average, are waiting in line? (Round your answer to 4 decimal places.)

c. How much time does a customer spend at the service desk (waiting plus service time)?

Explanation / Answer

This is a case of M/M/1 model. The following are the standard assumptions : 1. There is a single server with exponential service times and the service rate customers per time unit 2. Customers arriving according a Poisson process with the arrival rate customers per time unit 3. Number of waiting positions =

Given that arrival rate is 1/10 and service rate 1/ 3. The utilization factor ( U) would be arrival rate/ service rate = ( 1/10) / (1/3)= 3/10 or 0.33%

a. probability of waiting in line = U = 0.33% ( calculated above)

b. Number of customers, on average, waiting in line equals to U2/1- U = (3/10)2 /(7/10) = 9/70

c. average time a customer spends in waiting line waiting for the service (Wq) = Utilisation factor / service rate * (1- utilisation Factor) = (3/10) / (1/3 *7/10) = 9/7 = 1.28 minutes, total time spent by the customer at service desk = Wq + 1/ service rate = 9/7 + 3 = 4.28 minutes

c.

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